Volume 14, issue 2 (2010)

Download this article
Download this article For screen
For printing
Recent Issues

Volume 20
Issue 4, 1807–2438
Issue 3, 1257–1806
Issue 2, 629–1255
Issue 1, 1–627

Volume 19, 6 issues

Volume 18, 5 issues

Volume 17, 5 issues

Volume 16, 4 issues

Volume 15, 4 issues

Volume 14, 5 issues

Volume 13, 5 issues

Volume 12, 5 issues

Volume 11, 4 issues

Volume 10, 4 issues

Volume 9, 4 issues

Volume 8, 3 issues

Volume 7, 2 issues

Volume 6, 2 issues

Volume 5, 2 issues

Volume 4, 1 issue

Volume 3, 1 issue

Volume 2, 1 issue

Volume 1, 1 issue

The Journal
About the Journal
Editorial Board
Editorial Interests
Editorial Procedure
Submission Guidelines
Submission Page
Subscriptions
Author Index
To Appear
Contacts
ISSN (electronic): 1364-0380
ISSN (print): 1465-3060
Some remarks on the size of tubular neighborhoods in contact topology and fillability

Klaus Niederkrüger and Francisco Presas

Geometry & Topology 14 (2010) 719–754
Abstract

The well-known tubular neighborhood theorem for contact submanifolds states that a small enough neighborhood of such a submanifold N is uniquely determined by the contact structure on N, and the conformal symplectic structure of the normal bundle. In particular, if the submanifold N has trivial normal bundle then its tubular neighborhood will be contactomorphic to a neighborhood of N ×{0} in the model space N × 2k.

In this article we make the observation that if (N,ξN) is a 3–dimensional overtwisted submanifold with trivial normal bundle in (M,ξ), and if its model neighborhood is sufficiently large, then (M,ξ) does not admit a symplectically aspherical filling.

Keywords
neighborhoods of contact submanifolds, fillability
Mathematical Subject Classification 2000
Primary: 57R17
Secondary: 53D35
References
Publication
Received: 19 March 2009
Revised: 11 November 2009
Accepted: 5 November 2009
Published: 16 February 2010
Proposed: Leonid Polterovich
Seconded: Danny Calegari and Yasha Eliashberg
Authors
Klaus Niederkrüger
Klaus Niederkrüger
Institut de mathématiques de Toulouse
Université Paul Sabatier – Toulouse III
31062 Toulouse Cedex 9
France
Francisco Presas
Francisco Presas
ICMAT
CSIC
Facultad de Matematicas
Universidad Complutense de Madrid
Plaza de Ciencias no 3
28040 Madrid
Spain